Quiros, a native of Benahavis, made six birdies on the back nine, and his 62 matched the tournament single-round scoring record, set by Ricardo Gonzalez and Pablo Larrazabal at last year's tournament at Madrid's Club de Campo.
"I had 12 chances for birdie and I made 10 -- unbelievable," a surprised Quiros told reporters. "I think I was very lucky with the putter."
Garcia capped his 8-under 64 with an eagle at the par-5 18th hole.
"These (fairways) are comforting and you definitely see a difference coming out of the rough," Garcia said.
England's Oliver Fisher shot 7-under 65 and is alone in third place.
Defending champion Charl Schwartzel of South Africa shot 1-under 71.